[petsc-users] Algorithms to remove null spaces in a singular system

[Jed Brown]

Fande Kong <fdkong.jd at gmail.com> writes:
> Right now, we are forcing users to provide orthogonal basis vectors. Is
> there any issue if we orthogonalize  the arbibitry basis vectors provided
> by users in PETSc?  And then users could pass arbitrary basis vectors
> without doing any preprocessing.

The function currently does not copy the vectors (to save storage).  If
you want to orthogonalize the vectors, you will need to copy them.  If
doing that, it may be better to use Householder/TSQR -- Gram-Schmidt
doesn't produce particularly orthogonal matrices.  (There are a few
places in PETSc where Gram-Schmidt is naively assumed to produce a good
orthogonal basis even when there is no compelling cost reason for doing
so.  I know I'm guilty.)
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